Maximum entropy models for patterns of gene expression

Camilla Sarra, Leopoldo Sarra, Luca Di Carlo, Trevor GrandPre, Yaojun Zhang, Curtis G. Callan Jr., William Bialek
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Abstract

New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering or low-dimensional projections. Here we use the principle of maximum entropy to obtain a probabilistic description that captures the observed presence or absence of mRNAs from hundreds of genes in cells from the mammalian brain. We construct the Ising model compatible with experimental means and pairwise correlations, and validate it by showing that it gives good predictions for higher-order statistics. We notice that the probability distribution of cell states has many local maxima. By labeling cell states according to the associated maximum, we obtain a cell classification that agrees well with previous results that use traditional clustering techniques. Our results provide quantitative descriptions of gene expression statistics and interpretable criteria for defining cell classes, supporting the hypothesis that cell classes emerge from the collective interaction of gene expression levels.
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基因表达模式的最大熵模型
新的实验方法使同时测量数千甚至数百万个单个细胞快照中许多基因的表达水平成为可能。目前分析这些实验的方法包括聚类或低维投影。在这里,我们利用最大熵原理获得了一种概率描述,它捕捉到了在哺乳动物脑细胞中观察到的数百个基因的 mRNA 的存在或不存在。我们构建了与实验均值和成对相关性兼容的伊辛模型,并通过证明它能很好地预测高阶统计量来验证它。我们注意到细胞状态的概率分布有许多局部最大值。我们的结果提供了基因表达统计的定量描述和可解释的细胞类别定义标准,支持了细胞类别产生于基因表达水平的集体相互作用这一假设。
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